Research map / Probabilistic and scientific modeling / Causal discovery
Identifying Causal Effects Under Functional Dependencies
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Shows that knowing some variables are functionally determined by their parents can make unidentifiable causal effects identifiable and can reduce the set of observed variables needed, via a functional elimination operation and reduction to classical identifiability (ID/project-ID).
Problem
Causal effect identification in causal graphs with hidden variables when some variables are known to be functional (deterministic given parents) but their functions are unknown; positivity constraints complicate standard identification algorithms.
Approach
Introduces functional elimination (adding edges from parents to children and removing the functional variable), proves it preserves D-separation, marginal distributions and interventional distributions, and defines functional projection so that F-identifiability reduces to classical identifiability via the ID algorithm under suitable positivity constraints.
Key results
- Shows an example where P_x(y) is unidentifiable under strict positivity with hidden B but becomes identifiable as P_x(y)=sum_a P(a)P(y|a,x) when B is known to be functional.
- Proves functional elimination preserves D-separation: X and Y D-separated by Z in (G,W) iff d-separated in G' (Theorem on D-separation preservation).
- Proves that if every functional variable has at least one hidden parent, F-identifiability is equivalent to classical identifiability (Theorem on hidden-parent case).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Treat hidden variable B as functional | Causal effect of X on Y · Graph with observed A, X, Y | identifiability | Helped |
| Functionally project the graph by eliminating hidden functional variables before applying ID | Causal effect of X on Y · Graph with observed A, B, C, F, X, Y; hidden functional D and E | identifiability | Helped |
| Eliminate observed functional variable B when it satisfies the theorem's conditions | Causal effect of X on Y · Graph with observed A, B, C, F, X, Y; functional B | required observations | Helped |
| Use functional projection instead of classical projection for hidden functional variables | Causal graph projection · Observed A, B, G, H, I; hidden functional C, D | d-separation | Helped |
| Eliminate functional variables when every functional variable has at least one hidden parent | F-identifiability testing · Causal effects under the stated condition | identifiability | No clear effect |
| Pretend functional variables whose parents are observed are observed | F-identifiability testing · Causal effects with positivity on each treatment | identifiability | No clear effect |
Surprising findings
- An unidentifiable causal effect can become identifiable merely by knowing some hidden variable is functional, without knowing its function.
- Some observed functional variables can be excluded from observation without affecting identifiability of the causal effect.
Limitations
- Some reductions require positivity constraints (e.g., strict positivity) that may contradict functional dependencies, and the complete method only works under weak positivity with a new algorithm not yet available.
- Theorems apply only when all functional variables are hidden or when observed functional variables satisfy separability conditions; the general case is incomplete.
- Only discrete variables and qualitative functional dependencies are considered.
Experimental setup
Baselines: project-ID ID algorithm do-calculus
Builds on: ID algorithm project-ID do-calculus D-separation Bayesian network variable elimination
Closest papers by meaning
- Causal Effect Identifiability in the Presence of Latent Confounders Without Auxiliary Variables (ICML 2026 · similarity 0.92)
- Causal Effect Identifiability under Partial-Observability (ICML 2020 · similarity 0.92)
- Causal Identification under Markov Equivalence: Completeness Results (ICML 2019 · similarity 0.90)
- Causal Effect Identification in LiNGAM Models with Latent Confounders (ICML 2024 · similarity 0.89)
- On the Parameter Identifiability of Partially Observed Linear Causal Models (NeurIPS 2024 · similarity 0.89)
- Identifiability Guarantees for Causal Disentanglement from Purely Observational Data (NeurIPS 2024 · similarity 0.88)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.